Let's get the goodwill out of the way first. Government is coming closer to reflecting the gender proportions of society, and that can only be a good thing. The most inspired example is the appointment of Baroness Symons to the Ministry of Defence. No one doubts that she can deal with the intricacies - moral and political - of weapons procurement as well as her male predecessors.
I yearn to see the baroness's first meeting with the officials whom I met during the consultations for the Defence Review. The man seated to my right asked sympathetically: "Are you here to make a contribution, or just to learn?" After a long session on "Whither the UK's Global Reach", and the state of our aircraft carriers, another civil servant approached in the coffee break and murmured: "I hope this isn't all boring for you." Hell, no. I just passed the longueurs in the debate about restructuring Nato thinking with whether the pashmina was in or out, and how I was going to time the souffle just right for hubby.
The presence of greater numbers of women in the departments must go some way to redressing the expectations that men know stuff, while women are there, like books in a philistine's household, to help furnish the room. And yet there is something about the successful New Labour women which disturbs me, a persistent hint of the Stepford Wife syndrome. They are so well-behaved, so thoroughly unobjectionable. One thinks of Enid Blyton's description of the rather boring character in her Mallory Towers series - "solid, dependable Sally Hope". A lot of Ms Solid-Dependables have been promoted to the junior and middle ranks in the reshuffle - perfect delivery systems for whatever grand schemes male politicians have thought up.
Women have still not penetrated the inner sanctum of policy-making. Who does Mr Blair turn to when they plot grand strategy and rethink major initiatives? The A-team is Alastair Campbell; Chief of Staff Jonathan Powell; Policy Unit chief David Miliband, and the gone-but-never-forgotten Peter Mandelson. On the key area of education reform, he heeds his sound adviser, Andrew Adonis, and the Chief Inspector of Schools, Chris Woodhead. Women like Estelle Morris, who was deemed to have prospered as junior minister at Education, and Jacqui Smith, who takes her place, are judged on whether they can implement plans, placate teaching unions and front policies well in the media. They aren't the ones sitting down with Mr Blair to hammer out the next phase of the schools revolution.
It is easy to berate the women for on-message milk-soppery. They have simply learnt to play by the rules of the game imposed by others. As the new intake of women in Parliament discovered, the wisest strategy for advancement is to cultivate a loyalty which verges on the slavish, keep their pale-blue suits pressed ready for the call to appear on Newsnight, and steer well clear of controversy.
Hilary Armstrong, the Housing Minister, is a typically proficient representative of the breed. Last week, she was sent forth as a lone survivor of the meltdown at the Department of Environment, Transport and the Regions to reassure us that yet another wave of comings and goings was a sign of seamless normality, rather than a prime-ministerial panic about the standstills on New Britain's roads and on its railways.
Ms Armstrong is an impressive fire-fighter, and I sense that we will see more of the rising women deployed to reassure us that all is well and soothe away concerns. It is a political extension of the maternal role, applying sticking-plaster to sore areas of public life. But real power, it ain't. Ask yourself which women have the clout to change the Prime Minister's mind; the authority and status to be able to say to him that something is not working, that she has a better idea.
I can't think of a single one.
Even Mo Mowlam, the most lustrous of female Cabinet stars, has far more limited power than her high profile suggests. Her real usefulness was as a symbol of gutsy good-will and determination to get the Good Friday agreement the widest possible support in the communities of Northern Ireland. But when the hard men on both sides cut up rough over decom-missioning and the lamps burn late in Stormont, the Downing Street machine takes control of the process, and Mo is frankly irrelevant.
Few women take risks and win. One is the irrepressible Clare Short, who gets on because she is a good communicator, a useful link to the left, but most importantly because she doesn't give a damn and people rather like that. It also gives her a certain freedom to do her job, and not fret over where she stands in the hit parade of Number 10's affections. The rising generation lack this insouciance. They desperately want to have fulfilled careers in politics, just as their peers want the same advancement as men in journalism, business and the law.
Why shouldn't we - being no dimmer than the men and the beneficiaries of the earlier fights for women - want to be taken seriously?
But women still face a problem that dares not speak its name: the subtle but ingrained sexism of men who consider themselves blamelessly liberal and non-sexist. In this as in so many ways, Mr Blair is a modern Everyman. Socially, he is perfectly relaxed in female company. He is married to a highly successful and independently-minded partner. And yet the ambience of the inner circle of Government remains stubbornly male. The main bonding ritual is football. Mr Brown's kitchen cabinet is strictly boys' own.
Playing the numbers game by weighing the quantity of women in politics does not give an accurate picture of how much impact they have at the heart of affairs. I am unconvinced, for all the photo calls, that the men at the top really care about whether this is rectified - as long as the female head-count looks good in the media.
But just being there is no substitute for power. Look at Hillary Clinton. She wields considerable influence by virtue of her marriage to Bill. Yet she is prepared to risk the grind and possible, even probable, defeat standing for the US Senate against a popular mayor of New York. She does so because she wants to move from power-by-association to election on her own merits, to leave the shadows of patronage for the harsh lights of her own hustings. For the first time in many years, I find myself admiring her.